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<H2>DETAILS ON THE NUMERICAL TOOLS</H2>
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<p>Two numerical simulation codes were used to obtain
the numerical data: <A HREF="http://www.risoe.dk/vea-aed/numwind/index.htm"
TARGET="_blank"><tt><font size=+1>EllipSys2D</font></tt></A> and
<A HREF="http://raphael.mit.edu/xfoil/" TARGET="_blank">
XFOIL</A>.</p><br>

<h6><tt><font size=+1>EllipSys2D</font></tt></h6>
 
<p><A HREF="http://www.risoe.dk/vea-aed/numwind/index.htm" TARGET="_blank">
<tt><font size=+1>EllipSys2D</font></tt></A> is a numerical
Navier-Stokes flow solver. This code has been developed jointly
at DTU (<A HREF="http://www.afm.dtu.dk/" TARGET="_blank">Dept. of
Mechanical Engineering, Fluid Mechanics</A>) and Ris&oslash; by
<A HREF="http://www.afm.dtu.dk/Staff/jam/index.html"
TARGET="_blank">Jess Michelsen</A> and <A
HREF="http://met-hp-1.risoe.dk/cgi-bin/view.pl?id=94"
TARGET="_blank">Niels S&oslash;rensen</A>. It is designed to solve
the two-dimensional Navier-Stokes equations for an
incompressible fluid. It uses a cell-centered grid arrangement
for the pressure field and the cartesian velocity components. The
equations are discretised by means of a finite volume
formulation. The well-known velocity-pressure decoupling
is circumvented by using the Rhie and Chow interpolation
technique. The SIMPLE algorithm is used for solving the momentum
and pressure equations in a predictor-corrector fashion. The
convective terms were discretised by means of the second order
in space SUDS scheme (no limiter was used).</p>

<p>All the meshes that were used for the Navier-Stokes computations
presented in this database are C-meshes around the airfoils. They
were obtained by using the mesh generator <A
HREF="./../HTML/biblio.htm#SorensenHypGrid2D">HypGrid2D</A> developed
at Ris&oslash; by <A HREF="http://met-hp-1.risoe.dk/cgi-bin/view.pl?id=94"
TARGET="_blank">Niels S&oslash;rensen</A>.</p>

<p>Steady state computations were nearly always performed. However, in
a few cases, numerical instabilities prevent the convergence of the
computations. In these few cases, unsteady computations were
performed.</p>

<p>Turbulence was modelled by the <em>k</em>-&#969; (k-omega) SST
model by <A HREF="./../HTML/biblio.htm#Menter">Menter</A>. In
some cases, the flow was considered as fully
turbulent, i.e. the turbulent viscosity is directly given by
the turbulence model that is implemented in the numerical
code. In some other cases, a transition model
was used to account for the transition towards turbulence
phenomenon on the airfoil surface. Its purpose is to determine
a location along the surface of the airfoil, such that the flow
can be considered as laminar upstream this point, and as
transitional downstream. As a consequence, the turbulent viscosity
is switched off on the boundary layer stations upstream the
transition point. Downstream, the turbulent viscosity is given
by the turbulence model. However, in order to model the
turbulence intermittency that occurs in transitional flows, the
turbulent viscosity was weighted by a multiplicative factor that
grows from 0 (at the transition point) to 1 (at the end of the
transitional region) according to an empirical function given
by <A HREF="./../HTML/biblio.htm#ChenT">Chen and Thyson</A>. The
transition model by <A HREF="./../HTML/biblio.htm#Michel">Michel
</A> was used.</p><br>

<p>Further details on the numerical code and references for
the different numerical and modelling techniques can be found
in the <A HREF="./report.htm">Wind Turbine Airfoil
Catalogue</A> report itself, or in the following
references:<br>
<b>J.A. Michelsen</b>, Basis3D - A Platform for Development
of Multiblock PDE Solvers, <em>Tech. Report, Technical University
of Denmark, AFM 92-05</em>, 1992.<br>
<b>J.A. Michelsen</b>, Block Structured Multigrid Solution of 2D
and 3D Elliptic PDE's, <em>Tech. Report, Technical University of
Denmark, AFM 94-06</em>, 1994.<br>
<b>N.N. S&oslash;rensen</b>, General Purpose Flow Solver Applied
to Flow over Hills, <em>Tech. Report, Ris&oslash; National
Laboratory, Roskilde, Denmark, PhD
Thesis, Ris&oslash;-R-827(EN)</em>, June 1997.</p><br><br>

<h4>XFOIL</h4>

<p><A HREF="http://raphael.mit.edu/xfoil/" TARGET="_blank">XFOIL
</A> (written by <A HREF="./../HTML/biblio.htm#XFOIL">Prof. Mark
Drela</A> , MIT) is an interactive
program for the design and analysis of subsonic isolated
airfoils. It is based on a panel method combined with a viscous
boundary layer formulation. The wake simulation option was also
activated. The Reynolds number was set to the same value as
in the Navier-Stokes computations (see above). Note that
all computational data obtained with this code were performed
with a <b>transition model</b> that is using the Orr-Sommerfeld
transition criterion implemented in this code, <b>except</b> when
the results were compared with data originating from experiments
for which transition was triggered by a device on the airfoil. In
this last case, the transition was <b>fixed</b> at the same
location as in the experiment. In our case, airfoil surfaces were
always discretised into 120 panels.</p><br><br>

<br>
<p>Details on the specific computational conditions for each
airfoil can be found in the <A HREF="./report.htm">Wind Turbine
Airfoil Catalogue</A> report.</p><br>

<br>
<p><u><b><font color="#ff0000">IMPORTANT NOTE:</font></b></u> All
computational data are obtained from genuine 2D simulations. There
is no correction for tip-losses, or other correction or approximation.

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